Download Displacement currents in semiconductor quantum dots embedded

APPLIED PHYSICS LETTERS 91, 063114 共2007兲
Displacement currents in semiconductor quantum dots embedded
dielectric media: A method for room temperature photon detection
P. V. V. Jayaweera, A. G. U. Perera, and K. Tennakonea兲
Department of Physics & Astronomy, Georgia State University, Atlanta, Georgia and
Institute of Fundamental Studies, Hantana Road, Kandy, Central 20 000, Sri Lanka
共Received 14 June 2007; accepted 12 July 2007; published online 7 August 2007兲
It is shown that the high electronic polarizability of quantum dots can be utilized to devise photon
detectors by embedding quantum dots in dielectric media to form capacitors. Modulated light
generates displacement currents and an expression is obtained for responsivity in terms of the
properties of the quantum dot, the dielectric, and the detector geometry. A model detector
constituted of PbS quantum dots embedded in paraffin wax is devised to illustrate the principle,
giving ⬃0.6 A / W as an upper limit for the responsivity. As these systems sense only the variations
of the light intensity, they could be operated at ambient temperature. © 2007 American Institute of
Physics. 关DOI: 10.1063/1.2768305兴
The unique properties of low dimensional semiconductors offer opportunities for application in almost all areas of
electronics.1–5 Many concepts have been extensively studied
identifying potential applications. Quantum dots 共Qds兲 are
used in photon detection,1–3,6 especially the near infrared and
infrared 共IR兲 regions of the spectrum.7–10 Utilizing size quantized band gap modulation, Qds of low effective carrier mass
semiconductors can be sensitized to the electromagnetic
spectrum from ultraviolet to far IR. Photovoltaic and photoconductive photon detectors have been made from QD
blended conducting polymers.11–13 In photovoltaic detectors,
interpenetrating networks of polymer and Qds communicate
with two electrodes. The excitons generated by the incident
photons decompose at the interface into electron-hole pairs
which separate into the two regions creating a photocurrent
and a photovoltage. Photoconductive type operates by derivation of a current by an external voltage via movement of
carriers across the polymer medium. Properties of individual
Qds are greatly obscured by clustering and aggregation, and
also obtaining electronic contacts to Qds would not be an
easy task. The photoconductive detectors, where the Qds are
homogeneously impregnated into a solid substrate, avoid the
above problem. In this letter we show that by embedding
Qds in a film of high dielectric material to form a capacitor,
the displacement current generated by modulated light can
be used as a signal to detect photons. As in pyroelectric
detectors,14 this technique has the advantage that only the
intensity modulated light generates signals enabling room
temperature operation for sensing IR radiation. Again as in
photoconductive QD-polymer detectors, their fabrication
does not require electrical connections to the Qds. We illustrate the principle by designing a capacitor with PbS Qds
embedded in paraffin wax 关Fig. 1共a兲兴.
PbS Qds embedded paraffin wax films were prepared by
the following method. Water insoluble lead oelate was synthesized by mixing equal volumes of lead acetate 共0.1 M兲
and sodium oelate 共0.2 M兲 solutions. The white precipitate
of lead oelate was separated, washed with water, and dried in
a vacuum. A weighed amount of lead oelate was dissolved in
molten purified paraffin wax 共melting point ⬃64 ° C, dieleca兲
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tric constant= 2.4兲 and a thin layer of wax was spread on the
surface of a conducting glass plate 共1.5⫻ 1 cm2兲. After solidification of wax, the plate was inserted into a N2 atmosphere containing H2S 共⬃20% by volume兲 and propan-2-ol
vapor and left there for 2 h. H2S diffuses into the wax impregnating it with oleic acid capped PbS Qds. The presence
of the vapor of a slightly polar liquid 共propan-2-ol兲 facilitates
this diffusion controlled reaction. The absorption spectrum of
the film is presented in Fig. 1共b兲 and the spectrum of the film
material dissolved in hexane was also recorded. These spectra suggest a polydispersion PbS Qds in wax with a median
diameter of ⬃8 nm. To form the capacitor, the plate is
warmed to melt the wax and another conducting glass plate
posed above to cover an area of 1 cm2 and fill the capillary
space with molten wax. When wax solidifies, plates hold
together and leads are connected to the two protruding ends
of the conducting glass plates 共see inset of Fig. 1兲. The measured capacitance 共200 pF兲 of the system was nearly of the
same order as that of a capacitor of same dimensions 共area
= 1 cm2, thickness= 10 ␮m兲 with a film of pure wax and the
resistance exceeded 1 G⍀.
Calculations indicate that Qds have several orders of
magnitude larger polarizabilites than that of atoms and
molecules.15,16 This has been confirmed by quantum confined stark effect17,18 and measurement of the electronic polarizability of optically generated excitons in quantum dots.19
FIG. 1. 共Color online兲 共a兲 Absorption spectrum of the suspension of PbS
quantum dots. 共b兲 Cross section of the device experimentally tested.
0003-6951/2007/91共6兲/063114/3/$23.00
91, 063114-1
© 2007 American Institute of Physics
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063114-2
Appl. Phys. Lett. 91, 063114 共2007兲
Jayaweera, Perera, and Tennakone
FIG. 2. equivalent circuit of the detector and the circuit used for measurement of the photoresponse 共Cd = detector capacitance, Rd = detector
resistance兲.
Using effective medium theory,19,20 the electric susceptibility ␹ of the QD-dielectric composite can be expressed a
␹ = ␧0n␬␣ ,
␬=
共1兲
9␧2
,
共␧QD + 2␧兲2
共2兲
where n is the number density of excitions per QD, ␣ is the
exciton polarizability, ␧ is the dielectric constant of the composite, and ␧QD is the dielectric constant of the QD material.
Hence, if a capacitor of thickness s consisting of N Qds of
given size per unit volume is placed in a constant electric
field E, the displacement current density dD / dt = J共t兲 originating from time variation of n can be written as
J共t兲 =
dn
dD
= sN␧0␬␣E .
dt
dt
共3兲
For simplicity we analyze displacement current response of
the system assuming that the photon flux incident on the
capacitor modulates as I = I0共1 + sin ␻t兲. Thus the rate of exciton generation is given by
dn
= ␾I0关1 + sin共␻t兲兴 − kn,
dt
共4兲
where ␾ is the quantum efficiency of exciton formation and
k is the exciton recombination rate constant. Solving Eq. 共4兲
for n and combining with Eq. 共3兲, the displacement current
density can be expressed in the form
J共t兲 =
␾NEI0␻␬␣␧0
冑␻2 + k2
冉
sin共␻t + ␦兲 +
ke−kt
冑␻2 + k2
冊
,
共5兲
where tan ␦ = k / ␻ and we have set the initial condition
J共0兲 = 0, t = 0. When the transient in Eq. 共5兲 decays, the detector output current density simplifies to
J共t兲 =
␾NEI0␬␣␧0␻ sin共␻t + ␦兲
冑␻2 + k2
.
共6兲
Setting E = V / s 共V is the applied voltage bias兲, we obtain the
current 共A/W兲 and voltage 共V/W兲 responsivities of the detector 共RL and Rd as indicated in Fig. 2兲,
R=
冑2␾共␯兲␻VN␬␣␧0
,
h␯s冑␻2 + k2
FIG. 3. 共Color online兲 responsivity of the detector under different bias voltages. 共85 M⍀ resistor was used as load resistor RL and the chopping frequency was 57 Hz兲.
RV =
冑2␾共␯兲␻VN␬␣␧0 RL ⫻ Rd
⫻
.
RL + Rd
h␯s冑␻2 + k2
共7兲
The circuit used for the measurement of the photoresponse, including the equivalent circuit of the detector is
shown in Fig. 2. The effect of the parasitic capacitance in the
circuit is not very strong at low chopping frequencies 共i.e.,
␻ ⬍ 关RdCd兴1/2兲 The plot of responsitivity versus wavelength
at different bias voltages 共8.7– 40 V兲 and a fixed chopping
frequency of 57 Hz is shown in Fig. 3. Despite the simplicity
of the system, the response extends from 400 to 1100 nm.
For 共7兲 enables calculation of the intrinsic responsivity
of the detector in terms of the properties of the Qds, the
embedding dielectric medium, the thickness of the film, and
the bias voltage. Responsivity depends on several factors,
i.e., size and the number density of Qds, their polarizability,
the thickness of the capacitor, and the applied bias. The response increases linearly with the applied bias according to
Eq. 共6兲 up to ⬃20 V and deviation from linearity is seen
thereafter. A higher bias will also increase the noise and, at
biasing values exceeding the field ionization threshold, the
motion of dissociated electrons and holes will also contribute
to the displacement current, causing deviation from the linear
variation. Formula 共7兲 involves the recombination rate constant k which is sensitive to the structure of the dot 共i.e.,
capping, size, and shape兲 and its environment. Under optimum conditions 共i.e., absence of trapping of the carriers兲 the
exciton recombination is slow 共approximately millisecond
range兲 and the condition ␻ Ⰷ k should be satisfied. The constant k can be readily estimated from photocurrent transients
共when radiation of constant intensity is interrupted, the transient signal takes the form sN␬␣E␾Ioe−ikt兲 and the value
obtained is of the same order of magnitude 共i.e., milliseconds兲. For optimization of the responsivity, the quantum dots
need to be densely packed keeping the film thickness s comparable to the mean free path of photons. However, in general, conductor-insulator composites exhibit percolation
thresholds21 when the packing fraction of the conducting material exceeds a critical value N = NC. In the present system
such a threshold would depend on the size of the quantum
dots. We did not succeed in determining this threshold for
monodispersions of PbS Qds in paraffin. When the total
amount of PbS incorporated into the wax reached ⬃15% by
weight, PbS begins aggregating masking the detection of this
effect. Almost complete absorption of incident radiation
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063114-3
Appl. Phys. Lett. 91, 063114 共2007兲
Jayaweera, Perera, and Tennakone
avoiding any percolation threshold would be possible by increasing the film thickness. In general, near percolation
thresholds, systems tend to be noisy21 and therefore optimization should be achieved keeping N well below NC and
appropriate adjustment of s. In the present investigation no
attempt was made to optimize the system.
In the measurement reported, bias voltage was varied
from 1 to 40 V with a 85 M⍀ load resistor 共RL兲. Figure 3
gives the plot of voltage responsivity versus the wavelength
of the incident radiation and the responsitivity at the peak
absorption 共␭ = 540 nm兲 was found to be 195 V / W at a bias
of 40 V and the specific detectivity under the same condition
was determined as 3 ⫻ 108 cm Hz1/2 / W.
The responsivity of the present system can be compared
to that of a photoconductive detector of the same bulk material as follows. As photoconductive current density is Jc
= en␮E共␮ = e␶ / m兲, with ␮ the mobility, ␶ the scattering time,
m the carrier effective mass, and taking low frequency molecular exciton polarizability= e2 / ␧0m␻20 共␻0 exciton binding
energy/ប兲, we obtain J / JC = ␻sNA / ␶␻20 ⬃ 10−5 共with A the
detector area= 1 cm2, ␻ = 57 Hz, N = 107, and exciton binding
energy= 10 meV兲. Due to the less than ideal coverage of Qds
in the dielectric 共i.e., N = 107兲 the responsivity is very low
compared to a photoconductive detector. Owing to its low
melting point and brittleness, paraffin wax is not the best
material to embed Qds. However, due to the simplicity of the
preparation, paraffin wax was selected as the dielectric instead of any other dielectric material including silica, glass,
or polymers. Better methods of preparation of PbS Qds and
use of other embedding dielectrics should improve the performance, when N is increased by several orders of magnitude. It is straightforward to extend the concept proposed
here to Qds of other materials and nanowires. Carbon nanotubes which possess high polarizabilities22 with band gap
taliorability would provide an option to fabricate multiband
detectors. Thus more versatile photon detectors may be developed if nanotubes are used instead of quantum dots. An
additional merit is the sensitivity to polarized radiation if the
nanotubes are aligned in the dielectric medium. Furthermore,
large aligning torques can be applied to carbon nanotubes, in
a highly resistive dielectric medium compared to a conducting medium. The effects of multiexciton production will also
be reminiscent in these detectors, especially if PbS is replaced by PbSe. In PbSe-conducting polymer photon detectors, enhancements in quantum efficiency originating from
impact ionization have been observed.23
The optimization of the detectors based on this technique
requires further studies on quantum dot/nanotube impregnated dielectric media and assessment of noise and ways
minimizing it. It is also important to test the room temperature operability using Qds that absorb longer wavelengths.
Displacement current measurements in QD embedded dielectric media could also give useful information on properties of low dimensional semiconductors.
The authors wish to thank Steven Matsik for useful discussions. This work is supported in part by the NSF Grant
Nos. ECS 05-53051, INT-0322355, and OISE 0543257.
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